assign4_08

assign4_08 - The Chinese University of Hong Kong Department...

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The Chinese University of Hong Kong Department of Systems Engineering & Engineering Management ERG 2018 Advanced Engineering Mathematics (2008) Assignment 4 Question 1 Consider a 3 × 4 matrix A given as A = 1324 223 3 314 2 (a) Determine the rank of A and hence the dimensions of Nullspace( A )and Nullspace( A T ). (b) Show how you would obtain the vector bases for Rowspace( A ) and for Nullspace( A ), and verify the orthogonality between the two vector spaces. (c) Show how you would obtain the vector bases for Columnspace( A for Nullspace( A T ), and verify the orthogonality between the two vector spaces. (d) Construct diFerent ~y ’s to demonstrate that solving A~x = ~y can have a unique solution, no solution, or an in±nite number of solutions. Question 2 (a) Q. 12 of Section 7.1 (Kolman & Hill, 2008), p. 450. (b) Q. 20 of Section 7.1 (Kolman & Hill, 2008), p. 451. (c) Q. 13 of Section 7.2 (Kolman & Hill, 2008), p. 462. (d) Q. 20 of Section 7.3 (Kolman & Hill, 2008), p. 476. 1

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Question 3 A transportation company has a ﬂeet of 500 vehicles serving 3 cities A, B, and C. The current scheduling plan results in the following weekly
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This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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assign4_08 - The Chinese University of Hong Kong Department...

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